Archiv der Mathematik

, Volume 97, Issue 1, pp 17–24 | Cite as

A Boolean algebra of characteristic subgroups of a finite group

  • M. Deaconescu
  • I. M. Isaacs
  • G. L. Walls


We construct a “natural” sublattice L(G) of the lattice of all of those subgroups of a finite group G that contain the Frattini subgroup \({\Phi(G)}\) . We show that L(G) is a Boolean algebra, and that its members are characteristic subgroups of G. If \({\Phi(G)}\) is trivial, then L(G) is exactly the set of direct factors U of G such that U and G/U have no common nontrivial homomorphic image.

Mathematics Subject Classification (2010)

20D25 20D30 


Subgroup lattice Maximal subgroup Boolean algebra 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of MathematicsKuwait UniversitySafatKuwait
  2. 2.Department of MathematicsUniversity of WisconsinMadisonUSA
  3. 3.Department of MathematicsSoutheastern Louisiana UniversityHammondUSA

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